Asymptotic properties of solutions of nonlinear difference equations
نویسندگان
چکیده
منابع مشابه
Asymptotic Behavior of Solutions of Nonlinear Difference Equations
The nonlinear difference equation (E) xn+1 − xn = anφn(xσ(n)) + bn, where (an), (bn) are real sequences, φn : −→ , (σ(n)) is a sequence of integers and lim n−→∞ σ(n) =∞, is investigated. Sufficient conditions for the existence of solutions of this equation asymptotically equivalent to the solutions of the equation yn+1 − yn = bn are given. Sufficient conditions under which for every real consta...
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The authors consider themth order nonlinear difference equations of the form Dmyn+qnf(yσ(n)) = ei, where m ≥ 1, n ∈N = {0,1,2, . . .}, an > 0 for i= 1,2, . . . ,m−1, an ≡ 1, D0yn = yn, Diyn = an∆Di−1yn, i = 1,2, . . . ,m, σ(n) → ∞ as n → ∞, and f : R → R is continuous with uf(u) > 0 for u = 0. They give sufficient conditions to ensure that all bounded nonoscillatory solutions tend to zero as n→...
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Asymptotic properties of solutions of difference equation of the form ∆xn = anφn(xσ(n)) + bn are studied. Conditions under which every (every bounded) solution of the equation ∆yn = bn is asymptotically equivalent to some solution of the above equation are obtained. Moreover, the conditions under which every polynomial sequence of degree less than m is asymptotically equivalent to some solution...
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We study a scalar linear difference equation with several delays by transforming it to a system of Volterra equations without delays. The results obtained for this system are then used to establish oscillation criteria and asymptotic properties of solutions of the considered equation.
متن کاملEntire solutions of nonlinear differential-difference equations
In this paper, we describe the properties of entire solutions of a nonlinear differential-difference equation and a Fermat type equation, and improve several previous theorems greatly. In addition, we also deduce a uniqueness result for an entire function f(z) that shares a set with its shift [Formula: see text], which is a generalization of a result of Liu.
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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 1996
ISSN: 0377-0427
DOI: 10.1016/0377-0427(95)00139-5